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Simplifying 20 + 5x + -0.1x2 = 0 Solving 20 + 5x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -200 + -50x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -50x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -50x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -50x + x2 = 0 + 200 -50x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -50x + x2 = 200 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 200 + 625 Reorder the terms: 625 + -50x + x2 = 200 + 625 Combine like terms: 200 + 625 = 825 625 + -50x + x2 = 825 Factor a perfect square on the left side: (x + -25)(x + -25) = 825 Calculate the square root of the right side: 28.722813233 Break this problem into two subproblems by setting (x + -25) equal to 28.722813233 and -28.722813233.Subproblem 1
x + -25 = 28.722813233 Simplifying x + -25 = 28.722813233 Reorder the terms: -25 + x = 28.722813233 Solving -25 + x = 28.722813233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 28.722813233 + 25 Combine like terms: -25 + 25 = 0 0 + x = 28.722813233 + 25 x = 28.722813233 + 25 Combine like terms: 28.722813233 + 25 = 53.722813233 x = 53.722813233 Simplifying x = 53.722813233Subproblem 2
x + -25 = -28.722813233 Simplifying x + -25 = -28.722813233 Reorder the terms: -25 + x = -28.722813233 Solving -25 + x = -28.722813233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -28.722813233 + 25 Combine like terms: -25 + 25 = 0 0 + x = -28.722813233 + 25 x = -28.722813233 + 25 Combine like terms: -28.722813233 + 25 = -3.722813233 x = -3.722813233 Simplifying x = -3.722813233Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.722813233, -3.722813233}
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